The equation for the coordinate of a material point is given: x = 2 + 3t – 6t2. What is the form

The equation for the coordinate of a material point is given: x = 2 + 3t – 6t2. What is the form of the velocity equation for this material point?

Given:

x = 2 + 3 * t – 6 * t ^ 2 – the equation of motion of a material point.

It is required to find the equation for the change in the speed of this material point.

The equation for the change in speed is:

v (t) = v0 + a * t, where v0 is the initial velocity, a is the acceleration of the body.

From the equation of motion we find that v0 = 3 m / s, the acceleration is a = -12 m / s ^ 2. Then the equation of speed:

v (t) = 3 – 12 * t.

Also, the equation of speed can be derived from the derivative of the equation of motion.

Answer: v (t) = 3 – 12 * t.